Because liberal used to mean "supporting liberty" (the classical definition). But it has come to mean "agreeing with a certain set of beliefs and policies", and (recently) trying to de-platform anyone who publicly disagrees. And, in our bipolar political spectrum, those who disagree with the "liberals" are the "conservatives", who are therefore the ones the "liberals" are trying to de-platform.

So the "conservatives" believe very strongly in free speech (at the moment) because it's their speech that is currently getting crimped. And, seeing the trends, they think it's likely to get worse in the future. (As, say, anything disagreeing with the current "liberal" position gets labeled "racist" or "transphobic" or something, designed to make it virtuous to censor.)